November 3, 2023 7:00 am

The Science of Math Instruction: Incorporating Research-Based Instruction into Technology

Everyone’s talking about the science of reading, but what about mathematics? Take a look at agreed-upon best practices called cognitively-guided instruction, as well as technology that puts it into practice.

Teaching mathematics means more than introducing algorithms and procedures to students. Research shows that effective instruction also involves the development of a student’s conceptual understanding, mathematical reasoning, and problem-solving skills.

One research-based approach to mathematics instruction is Cognitively Guided Instruction (CGI), as described in Children’s Mathematics: Cognitively Guided Instruction (Carpenter et al., 2014). CGI shifts an educator’s focus away from direct instruction and toward understanding an individual student’s mathematical thinking. The teacher then leverages this understanding as the foundation to guide the student toward increasingly complex concepts.

Now, as online programs gain popularity in today’s classrooms, schools have the opportunity to choose technology that not only supports students’ procedural fluency but also aligns with research-based principles to develop students’ conceptual understanding. By evaluating the technology we bring to students through the lens of a framework such as CGI, we can help ensure that students have the opportunity to develop the skills they need to succeed beyond memorization.

What is Cognitively Guided Instruction (CGI)?

CGI is an approach to teaching mathematics that focuses on students’ critical thinking and problem-solving. Instead of just showing students how to solve a problem, teachers guide students to explore strategies and approaches that make sense from their unique understanding of a situation. The following are just some of the principles of CGI, as highlighted in Children’s Mathematics (Carpenter et al., 2014).

Problem Solving: Students are encouraged to tackle problems using critical thinking and creativity before receiving direct instruction. Given a story problem anchored in a real-world context familiar to students (such as sharing a food item among friends), students reason using a strategy of their choice.
Teacher as a Facilitator: Teachers transition away from the role of traditional instructors and toward the role of facilitators. They listen to students’ strategies, pose thought-provoking questions, and steer discussions while providing opportunities for students to learn from their peers’ thought processes.
Building on Prior Knowledge: Students bring their experiences and understandings into the classroom. Teachers leverage each student’s prior knowledge as a foundation and layer new concepts on top of the ideas that students have already grasped.

Applying CGI to Online Learning

When designed with research-based principles in mind, online programs have the ability to increase accessibility to effective instruction. For example, the following characteristics of various online programs provide the flexibility to support CGI practices.

Adaptive Learning Environments: Adaptive learning environments powered by algorithms can provide students with a personalized learning experience that caters to their unique needs and preferences. By analyzing a student’s performance and feedback, online platforms can generate customized content tailored to their strengths and weaknesses. This approach to learning aligns with CGI’s emphasis on personalized education, which recognizes that every student has a unique learning style and pace.
Virtual Manipulatives: Utilizing virtual tools, such as base-ten blocks, offers students an interactive experience to experiment with variables and visualize outcomes. This approach enables them to select the appropriate device that aligns with their current understanding and apply critical thinking and creativity to solve a given problem.
Real-world Problem Solving: Online platforms can offer practical problem-solving exercises that mirror real-life challenges. This approach aligns with cognitively guided instruction’s emphasis on applying mathematical concepts to everyday situations. By bridging the gap between theory and practical significance, students can gain a deeper, contextual understanding of mathematics and its relation to the world around them.

By incorporating CGI practices with online platforms’ capabilities, we can anchor each student’s learning experience in student-centered, data-driven instruction.

The Idaho Study: A Snapshot of Research-Based Technology in Action

Imagine Math ISAT Performance Research Brief

Read the Full Study

Imagine Math is one supplemental, personalized online program that incorporates the features highlighted above. It presents students with problems, equips them with virtual tools, and adapts its levels of support in response to students’ answers. “Imagine Math’s personalized learning platform aligns with each student’s needs while providing the right amount of challenge to help the student achieve grade-level proficiency,” said Sari Factor, Chief Strategy Officer at Imagine Learning (New Study Reveals Significant Gains in Student Math Performance with Imagine Math, 2023).

This year, a study was conducted to assess the impact of Imagine Math on students’ academic performance. The study analyzed over 4,000 math assessment scores from the Idaho State Assessment Test (ISAT) of students in grades 4 through 8. The assessment scores were taken from schools across four different districts in Idaho during the 2021-22 academic year. Key takeaways from the research include:

The relationship between Imagine Math lessons passed, and ISAT score growth is positive for all grades and statistically significant for grades 4 through 7.
Positive and significant relationships between Imagine Math lessons passed and ISAT math score growth for various student subgroups, including special education students, English learners, students eligible for free or reduced-price lunch, and Hispanic/Latino or American Indian/Alaskan Native students.

These findings underscore the potential of platforms like Imagine Math that align with student-centered methodologies to enhance student outcomes.

The Future of Math Instruction

In today’s rapidly evolving society, education has significantly shifted due to technological advancements and a more comprehensive understanding of how individual students learn. By leveraging technology that incorporates research-based instruction, educators can create a more engaging and effective learning experience for students, leading to better academic outcomes and a more promising future.

About the Author – Erin Springer

Erin Springer is a former elementary school teacher who transitioned to supporting other teachers as a Professional Development Specialist at Imagine Learning. She is enthusiastic about helping teachers use educational technology to improve student outcomes, save time, and understand students’ needs.

Citations:

Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (2014). Children’s Mathematics: Cognitively Guided Instruction (2nd ed.). Heinemann.

Imagine Learning. (2023, June 20). New Study Reveals Significant Gains in Student Math Performance with Imagine Math [Press release]. https://www.imaginelearning.com/press/study-reveals-significant-gains-student-math-performance-imagine-math/

September 7, 2023 10:21 am

Soft Skills with Big Impact: the 4Cs of STEM

Make STEM classrooms a playground for curiosity, a canvas for creativity, a stage for communication, and a hub for collaboration. When students embrace these skills, they’re not just preparing for the future — they’re shaping it.

“Hey Siri, how many rings does Saturn have?”

“Alexa, tell me what the square root of 1089?”

“ChatGPT: give me HTML code to embed a basic calculator on a webpage.”

There was a day when students had to ask their teachers, librarians, or even consult an encyclopedia for this type of information. But those days are long (like really long) gone, and the teacher is no longer the only keeper of information in the room.

Since the teacher’s role is evolving due to new technologies, and certainly students are not motivated to memorize what Alexa already knows, what should STEM classrooms be focused on? What skills are employers in STEM careers looking for if ChatGPT can produce code for free?

A 2018 survey by the Association of American Colleges & Universities showed, “that just 34 percent of top executives and 25 percent of hiring managers say students have the skills to be promoted. Many of those skills are soft skills — communication, team work, problem-solving — that are critical in a quickly shifting job market. Entry-level skills change every few years; it’s the habits of learning to learn and navigating the ambiguity of a career that will prove most valuable to undergraduates in the long run.”

The National Education Association has boiled these soft skills down to the 4 Cs: Creativity, Critical Thinking, Communication, and Collaboration. Let’s explore why these 4Cs are critical to providing a modern STEM education that gives students real career opportunities.

1. Critical Thinking: where curiosity begins

Imagine a classroom buzzing with questions. Except, not fact-based “how many rings does Saturn have” questions. Questions like: is it possible for New York City to become carbon neutral? What would that plan look like? Or: why does the kind of water (fresh or salt) affect how long it takes an ice cube to melt? That’s the power of critical thinking at work. It’s all about encouraging young minds to ask, “Why?” and “How?” Critical thinkers don’t just accept things at face value; they dig deeper. When students learn to analyze information, separate facts from opinions, and spot patterns, they become problem-solving heroes.

Picture a group of students exploring a science experiment. Instead of just following a set of instructions, they’re asking themselves, “What will happen if we change this variable?” That’s critical thinking igniting their imagination — it’s like a spark that lights up their learning journey.

2. Creativity: where imagination takes flight

Creativity isn’t just for artists — it’s a skill that every STEM student needs. It’s about looking at a problem from a different angle and dreaming up new solutions. Think of it as the magic wand that turns ordinary ideas into extraordinary ones.

Take a moment to think about a famous inventor, like Thomas Edison. He didn’t just stumble upon the light bulb; it took him 1000 attempts to find a design that worked. Creativity is what made him keep going, even when things got tough. Encouraging our students to think outside the box, to come up with wild ideas, and to believe that they can change the world — that’s the heart of creativity in STEM education.

3. Communication: bridges between minds

Imagine a world where nobody understood each other. It would be chaotic, right? Communication is like a bridge that connects our thoughts to the world. In STEM, it’s not enough to have brilliant ideas; you also need to share them effectively.

Think about a young engineer who designs an amazing new gadget. If they can’t explain how it works to others, their idea might never see the light of day. Teaching students how to express complex ideas in simple terms empowers them to inspire, collaborate, and bring their innovations to life.

4. Collaboration: teamwork for triumph

Remember the saying, “Two heads are better than one”? That’s the spirit of collaboration. In a world where problems are more complex than ever, working together is key. Collaboration is like a puzzle; each piece has its role, and when they come together, they create something amazing.

Think about a group of students working on a science project. Some are great at designing, others excel at research, and a few are natural leaders. When they pool their talents, their project becomes a masterpiece. It’s the same spirit that built the tallest skyscrapers and sent humans to the moon.

Putting the 4Cs into action

Imagine a classroom where students use their critical thinking skills to solve a real-world problem. Maybe they’re designing a water-saving system for their school garden. They brainstorm creative ideas, like using rainwater and self-watering plants. Then, they work as a team to build the system and explain their design to their classmates. These students are embracing the 4Cs in action: critical thinking, creativity, communication, and collaboration.

Empowering educators for success

As educators, you’re the guides on this exciting journey. You hold the keys to nurturing the 4Cs in your students. Encourage them to question, to dream, to share, and to work together. Make STEM education a playground for curiosity, a canvas for creativity, a stage for communication, and a hub for collaboration.

When students embrace these skills, they’re not just preparing for the future — they’re shaping it.

Imagine Learning STEM

Prepare the next generation of STEM leaders with digital and hands-on learning aligned to the 4 Cs.

Tell Me More

About the Author – Carolyn Snell

Carolyn Snell started her career in education teaching first grade in San Bernardino, California. A passion for the way technology and stellar curricula can transform classrooms led her to various jobs in edtech, including at the Orange County Department of Education. Her knack for quippy copy landed her a dream job marketing StudySync—an industry leading ELA digital curriculum. Now, as the Senior Content Marketing Manager for Imagine Learning, Carolyn revels in the opportunity to promote innovative products and ideas that are transforming the educational space for teachers and students.

September 4, 2025 8:00 am

New Mexico Approves Imagine Learning Illustrative Mathematics for Statewide K–12 Math Adoption

Core math curriculum supports state’s instructional vision and helps teachers foster deep mathematical understanding.

September 4, 2025 – Tempe, AZ — Imagine Learning is proud to announce that Imagine Learning Illustrative Mathematics, the leading problem-based core math curriculum, has been officially approved for statewide adoption in New Mexico.

This adoption affirms Imagine Learning’s commitment to delivering high-quality instructional materials that support math achievement through exploration, reasoning, and real-world relevance.

“We are honored to support New Mexico’s math educators with a curriculum designed to empower student thinking,” said Kinsey Rawe, EVP and Chief Product Officer at Imagine Learning. “Imagine Learning Illustrative Mathematics aligns to the state’s instructional vision and gives teachers the tools they need to foster deep mathematical understanding.”

About Imagine Learning Illustrative Mathematics

Imagine Learning Illustrative Mathematics is a K–12 core curriculum built on the foundations of coherent content, equitable access, and classroom-centered instruction. Designed by educators for educators, the curriculum includes:

State standards alignment across all grade levels
Structured math discourse routines that build student confidence
Real-world tasks that engage and connect learning to students’ lives
Extensive teacher resources, including lesson narratives, pacing guides, and embedded assessments

As an IM Certified® Partner, Imagine Learning provides an unparalleled resource for both teachers and students, offering enhanced materials designed to support educators in planning and conducting lessons across diverse instructional settings. Available in both print and digital formats, the curriculum supports flexible implementation models across diverse learning environments.

New Mexico Districts Can Now Begin Review for 2026 Implementation

With Imagine Learning Illustrative Mathematics officially adopted, districts throughout New Mexico are now encouraged to begin review and planning for full implementation in the 2026 school year.

District teams can access full sample materials, alignment documentation, and professional learning plans to guide their evaluation and adoption process. To begin your review, visit imaginelearning.com.

About Imagine Learning

Imagine Learning creates K–12 learning solutions that support the boundless potential of students in more than half the districts nationwide. Empowered with data and insights from educators, we innovate to shape the future of education with a robust, digital-first portfolio of school services and core, courseware, and supplemental solutions. Learn more: imaginelearning.com.

September 3, 2025 8:00 am

Dragonfly Takes Flight: Imagine Learning Launches a Next-Generation K–5 Literacy Program That Brings Knowledge to Life

New core English Language Arts solution combines skills, knowledge, and dynamic media to prepare students for the future.

Tempe, Arizona — September 3, 2025 — Imagine Learning, the nation’s largest provider of digital K–12 curriculum solutions, today announced the launch of Dragonfly, a new K–5 English Language Arts program designed to put knowledge at the center of literacy instruction.

In today’s classrooms, the need for deep, connected knowledge has never been greater. Research shows that students become stronger readers when they build background and vocabulary across rich, meaningful topics. Dragonfly makes this possible by pairing the science of reading with authentic texts, explicit skills, and original media in a clear, consistent structure that makes high-quality instruction easier to deliver — and creates a literacy experience that builds skills and knowledge together, every single day.

“Our goal in creating Dragonfly was to design a curriculum that truly engages and challenges young learners — teaching reading in a way that sparks imagination and fuels curiosity about the world,” said Robert Romano, GM of Core Humanities at Imagine Learning. “Knowledge is the key to understanding. By blending skills instruction, authentic texts, and dynamic media, Dragonfly empowers students to make connections, think critically, and develop a deeper understanding of their world and their place in it.”

Why Knowledge Matters — Lift Off with Dragonfly

Too often, literacy instruction focuses only on discrete skills, leaving students without the background knowledge that fuels comprehension. Dragonfly changes that. Each module is rooted in content-rich topics that broaden students’ horizons while strengthening the reading, writing, speaking, and listening skills that unlock future learning.

With Dragonfly, teachers and students can expect:

For Teachers:

Ready-to-teach lessons with built-in modeling and knowledge-based instruction
A digital platform for planning, delivery, and progress monitoring
Seamless print and digital integration for classroom flexibility
Foundational skills options for whole-group, small-group, and independent learning

For Students:

Authentic texts and engaging knowledge-rich themes
Dynamic media like Discovery Point, Sound Safari, and WingsTV
Daily opportunities to read, write, speak, and collaborate around big ideas

“Every classroom is full of unique learners, and every teacher is balancing limited time with big expectations,” said Kinsey Rawe, EVP and Chief Product Officer at Imagine Learning. “Dragonfly was built to meet students where they are, providing the right support at the right time, and set them up with the knowledge and skills they need to thrive in literacy, not just in school, but in life.”

A Literacy Program That Connects the Dots

Dragonfly’s Knowledge Building and Foundational Skills program unites phonics, fluency, comprehension, writing, speaking, and listening into one clear instruction arc — while ensuring every activity builds towards deeper understanding. With embedded assessments, tools for real-time differentiation, and consistent instructional routines, Dragonfly will inspire confidence in educators and give students purpose.

Ready to Lift Off with Literacy and See Knowledge in Action?

Be among the first to take flight with Dragonfly! Starting in the 2025–26 school year, pilots will be available in school districts nationwide, with full classroom availability coming in 2026–27. Explore samples, digital previews, and more now at ImagineLearning.com/Dragonfly

About Imagine Learning

August 27, 2025 9:00 am

Imagine Learning Earns Certification in Rivet Education’s Professional Learning Partner Guide

Imagine Learning joins elite network of professional learning organizations that helps school districts identify high-quality, curriculum-based partners.

Tempe, AZ — August 27, 2005 — Imagine Learning, a leading provider of K–12 digital-first core, supplemental, and intervention solutions, today announced its certification as a provider in Rivet Education’s Professional Learning Partner Guide (PLPG), a trusted national resource that helps school districts identify high-quality, curriculum-based professional learning partners.

The certification distinguishes Imagine Learning as part of an elite network of nearly 60 professional learning organizations nationwide. Together, these organizations support over 80% of the most widely used high-quality instructional materials (HQIM) across the country. For districts, inclusion in the PLPG signals that a provider has passed a rigorous, three-step evaluation process assessing HQIM expertise, quality of professional learning design, and the use of data to inform continuous improvement.

“Being recognized in the Professional Learning Partner Guide underscores our deep commitment to empowering teachers and leaders with the tools, strategies, and support they need for student success,” said Krysia Lazarewicz, VP of Professional Learning & Development and Customer Success at Imagine Learning. “This certification affirms the strength of our curricula-aligned professional learning and its measurable impact in classrooms nationwide.”

Now in its fifth year, the PLPG is accessed by more than 70,000 decision-makers annually and is increasingly required by states for contract eligibility. Imagine Learning joins nearly 60 professional learning organizations featured in the guide, collectively serving more than 80% of widely used HQIM across the country.

The recognition aligns with Imagine Learning’s mission to inspire learning breakthroughs for every student by ensuring educators have the support they need to drive successful curriculum implementation.

About Imagine Learning

About Rivet Education’s Professional Learning Partner Guide

The Professional Learning Partner Guide is a vetted, national list of organizations that provide high-quality, curriculum-based professional learning services. Inclusion signifies that a provider has demonstrated evidence of strong HQIM expertise, robust design, and a continuous improvement mindset. The guide helps educators quickly connect with trusted partners for adoption, implementation, and sustainability of instructional materials. Explore the guide at plpartnerguide.org.

Spanish Audio Tracks Now in Imagine EdgeEX

August 2025

Imagine EdgeEX now includes Spanish audio tracks across all science, math, and social studies courses. These tracks help Spanish-speaking students better access and engage with content, while giving educators a practical way to support multilingual learners across subjects.

Learn More

New Custom Activity Options in Imagine EdgeEX

August 2025

Add Custom Activities with set timing and custom directions

Educators using Imagine EdgeEX can now create Speaking Activities in addition to Writing Prompts and Projects. Custom activities support flexible instruction, with options to include directions and set expected completion times, helping educators tailor learning experiences for each class.

Learn More

Expanded AI Grading Assistant – now for Essays too!

August 2025

Provide AI-powered, rubric-based feedback on student essay

The AI Grading Assistant in Imagine EdgeEX now supports essays. Educators can generate rubric-based suggested comments to give students timely, constructive writing feedback—saving time and helping improve writing instruction across subjects.

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Proctorio Lockdown Browser Now Available in Edgenuity and EdgeEX

August 2025

Secure student assessments by restricting browser activity during testing

Educators using Imagine Edgenuity® or Imagine EdgeEX can now enable the Proctorio Lockdown Browser for quizzes, tests, and exams. This tool helps maintain academic integrity by locking students into the assessment window and blocking new tabs, extensions, and scripts, creating a more secure, distraction-free testing experience.

Learn More

New Character Replacement Alert in Plagiarism Scanner

August 2025

Enhanced Plagiarism Detector

An enhanced kind of cheat detection is now available to customers who utilize the Plagiarism and AI Scanner. The PDF report will now include a “Character Replacement” Alert when the scanner suspects the possible use of special characters in order to manipulate the scan.

Learn More

Smarter Placement in Imagine MyPath

August 2025

Students now start at their assessed level for more efficient learning

Imagine MyPath® now launches students placed above grade level directly into content that matches their assessed ability—skipping lessons they’ve already mastered. This update streamlines learning paths, helping students progress more quickly. Educators can also choose where placement starts using a new toggle in the Placement Modal.

Learn more

New for Fall: Live Spanish Instruction with Intelli-Sync

August 2025

Live instruction and layered support for Spanish I & II

This fall, Intelli-Sync expands to include Spanish I and II — high school world language courses taught by certified Spanish teachers. Whether you’re solving for staffing gaps or expanding course offerings, Intelli-Sync ensures consistent, high-quality instruction.

Students receive layered support through:

Weekly, live class sessions
1:1 and small group sessions
24/7 online coursework
On-demand tutoring

What is Cognitively Guided Instruction (CGI)?

Applying CGI to Online Learning

The Idaho Study: A Snapshot of Research-Based Technology in Action

The Future of Math Instruction

About the Author – Erin Springer

Citations:

1. Critical Thinking: where curiosity begins

2. Creativity: where imagination takes flight

3. Communication: bridges between minds

4. Collaboration: teamwork for triumph

Putting the 4Cs into action

Empowering educators for success

Imagine Learning STEM

About the Author – Carolyn Snell

Support Spanish-speaking students in science, math, and social Studies

Add Custom Activities with set timing and custom directions

Provide AI-powered, rubric-based feedback on student essay

Secure student assessments by restricting browser activity during testing

Enhanced Plagiarism Detector

Students now start at their assessed level for more efficient learning

Live instruction and layered support for Spanish I & II